4.45.35 $-y^{‴}(x)+y^{⁗}(x)-3y^{″}(x)+5y^{\prime }(x)-2y(x)=e^{3x}$

ODE
$$-y^{‴}(x)+y^{⁗}(x)-3y^{″}(x)+5y^{\prime }(x)-2y(x)=e^{3x}$$ ODE Classification

[[_high_order, _with_linear_symmetries]]

Book solution method
TO DO

Mathematica ✓
cpu = 0.0345105 (sec), leaf count = 39

$$\left\{\{y(x)\to c_1{e}^{-2x}+e^x(x(c_{4}x+c_3)+c_2)+\frac{e^{3x}}{40}\}\right\}$$

Maple ✓
cpu = 0.018 (sec), leaf count = 33

$$\{y\left(x\right)=\frac{{\mathrm{e}}^{3x}}{40}+\mathit{\_}\mathit{C}\mathit{1}{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{2}{\mathrm{e}}^{-2x}+\mathit{\_}\mathit{C}\mathit{3}x{\mathrm{e}}^x+\mathit{\_}\mathit{C}\mathit{4}{x}^2{\mathrm{e}}^x\}$$ Mathematica raw input

DSolve[-2*y[x] + 5*y'[x] - 3*y''[x] - y'''[x] + y''''[x] == E^(3*x),y[x],x]

Mathematica raw output

{{y[x] -> E^(3*x)/40 + C[1]/E^(2*x) + E^x*(C[2] + x*(C[3] + x*C[4]))}}

Maple raw input

dsolve(diff(diff(diff(diff(y(x),x),x),x),x)-diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+5*diff(y(x),x)-2*y(x) = exp(3*x), y(x),'implicit')

Maple raw output

y(x) = 1/40*exp(3*x)+_C1*exp(x)+_C2*exp(-2*x)+_C3*x*exp(x)+_C4*x^2*exp(x)